2420.21 – Horses and Oats

A farmer is going to the state fair to enter his horses in the long face competition. How much food should he take? Nine bags of oats feed his $8$ horses for $7$ days. He is taking $5$ horses to the contest for a total of $4$ days. Will $6$ bags of oats be enough?

Solution

Since $9$ bags last $8$ horses $7$ days, $6$ bags will last 8 horses $2/3$ as long, that is for $2/3 \times 7 = 14/3 = 2 2/3$ days. By the same kind of thinking, 6 bags will last 5 horses 8/5 times longer, that is, for $8/5 \times 14/3 = 112/15 = 7 7/15$ days (roughly a week).

More than enough! So $6$ bags of oats will be sufficient. He could get by with fewer bags. (Ha, but how many fewer?)